$$3x\cdot2-9\cdot\dfrac{x}{12}x\cdot2=\dfrac{-18x^2+72x}{12}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3x\cdot2-9 \cdot \frac{x}{12}x\cdot2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}6x-9 \cdot \frac{x}{12}x\cdot2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}6x-\frac{9x}{12}x\cdot2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}6x-\frac{9x^2}{12}\cdot2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}6x-\frac{18x^2}{12} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{-18x^2+72x}{12}\end{aligned} $$ | |
| ① | $$ 3 x \cdot 2 = 6 x $$ |
| ② | Multiply $9$ by $ \dfrac{x}{12} $ to get $ \dfrac{ 9x }{ 12 } $. Step 1: Write $ 9 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 9 \cdot \frac{x}{12} & \xlongequal{\text{Step 1}} \frac{9}{\color{red}{1}} \cdot \frac{x}{12} \xlongequal{\text{Step 2}} \frac{ 9 \cdot x }{ 1 \cdot 12 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 9x }{ 12 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{9x}{12} $ by $ x $ to get $ \dfrac{ 9x^2 }{ 12 } $. Step 1: Write $ x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{9x}{12} \cdot x & \xlongequal{\text{Step 1}} \frac{9x}{12} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 9x \cdot x }{ 12 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 9x^2 }{ 12 } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{9x^2}{12} $ by $ 2 $ to get $ \dfrac{ 18x^2 }{ 12 } $. Step 1: Write $ 2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{9x^2}{12} \cdot 2 & \xlongequal{\text{Step 1}} \frac{9x^2}{12} \cdot \frac{2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 9x^2 \cdot 2 }{ 12 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 18x^2 }{ 12 } \end{aligned} $$ |
| ⑤ | Subtract $ \dfrac{18x^2}{12} $ from $ 6x $ to get $ \dfrac{ \color{purple}{ -18x^2+72x } }{ 12 }$. Step 1: Write $ 6x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: To subtract raitonal expressions, both fractions must have the same denominator. |